Question

Medical researchers found that the risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases. The risk of having a car accident due to alcohol consumption is modeled by the function R(x)= 6e^12.77x where x is the blood alcohol concerntration, and R(x), given as percent, is the tiek of having a car accident.

= = Heeeng Subde Emph. Emphasis Medical researchers found that the risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases. The risk of having a car accident due to alcohol consumption is modeled by the function R(x) = 6e1277x where x is the blood alcohol concentration, and R(x), given as percent, is the risk of having a car accident Part 1: The graph of this exponential model is provided below. By using the graphical approach, answer the following questions: 1001 R(x) 90 80 70 60 Risk of a Car Accident % 50 40 30 20 10 002 0.04 006 0.08 0.1 0.12 0.14 016 Blood Alcohol Concentration O 18 02 022 1) Determine the domain and the range. ii) Approximately, what is the risk of a car accident when there is a blood alcohol concentration of 0.162 iil) Approximately, what is the blood alcohol concentration when there is a 60% risk of a car accident?

Answer 1

The solution is given below

Part-1 (I) From the graph we can see that can see (II) We the graph Domain = [0, 0.221 and Range -lo, loo that when x=0,16 46 approximately So, when' x=0.16 blood alcohol concentration thin the chance car accident is 46.1 takes value y of (II) We can see that at So, when there graph meets for yo Go the x=0.10 on k-anis. 60% chance blood alcohol 0.10 of Car accident, then the will be Part-2) (I) comparing The given model is R(x) = 6el2778 the givin model with R(x) = Roeax is r=12.77 So, the growth rate e = 2.0432 (II) when o.16 then R(0.16) 6 ell2.77X0.16) 6 e2 36(7.71525956) R(0.16 46.291551 R(0.16) = 46.29 So, when blood alcohol concentration is 0.16 then chance car accident is 46.29 1 Or of

Gozo e 12.77 se (II) when car accident chance is 60% then » 2016 = €12.77% 1o.-e 12,778 > en Clo) = ln (e 12.778) 12.778= ln (lo) x=0.100312066 xz0.18 So blood alcohol concentration is 0.18 when car accident chance 607, y xz en Clo) /12.17 IS